Traditional spectroscopic methods are limited in sensitivity to approximately one part per ten thousand (1:10.sup.4) to one part per hundred thousand (1:10.sup.5). The sensitivity limitation arises from instabilities in light source intensity that are translated into noise in the absorption signal. For general information on traditional spectroscopy methods see for example Dereniak and Crowe, Optical Radiation Detectors, John Wiley & Sons, New York, 1984, and Demtroder, Laser Spectroscopy, Springer, Berlin, 1996.
Cavity lifetime spectroscopy, otherwise known as Ring-Down Spectroscopy (CRDS), a technique first described by O'Keefe and Deacon in an article in Rev. Sci. Instrum. 59(12):2544-2551 (1988), allows one to make absorption measurements with sensitivities on the order of one part per ten million (1:10.sup.7) to one part per billion (1:10.sup.9) or higher. For general information on CRDS see U.S. Pat. No. 5,528,040 by Lehmann, as well as the articles by Romanini and Lehmann in J. Chem. Phys. 102(2):633-642 (1995), Meijer et al. in Chem. Phys. Lett. 217(1-2):112-116 (1994), Zalicki et al. in App. Phys. Lett. 67(1):144-146 (1995), Jongma et al. in Rev. Sci. Instrum. 66(4):2821-2828 (1995), and Zalicki and Zare in J. Chem. Phys. 102(7):2708-2717 (1995).
In a CRDS system, the sample (absorbing material) is placed in a high-finesse stable optical resonator or ring-down cavity having an input coupling mirror and an output coupling mirror. Light admitted into the ring-down cavity through the input coupler circulates back and forth multiple times setting up standing waves having periodic spatial variations. Light exiting through the output coupler is proportional to the intracavity light intensity.
After the input light source is terminated, the radiant energy stored in the ring-down cavity decreases in time (rings-down). For an empty cavity, the stored energy follows an exponential decay characterized by a ring-down rate that depends only on the reflectivity of the mirrors, the separation between the mirrors and the speed of light in the cavity. If a sample is placed in the resonator, the ring-down is accelerated; under suitable conditions, the intracavity energy decays almost perfectly exponentially. An absorption spectrum for the sample is obtained by plotting the ring-down rate R or the reciprocal of the ring-down decay constant 1/.tau. versus the wavelength .lambda. of the incident light.
In comparison to conventional spectroscopic techniques, CRDS promises to achieve extremely high detection sensitivity because the ring-down rate 1/.tau. is not a function of the intensity of the incident light. In other words, intensity fluctuations of the incident light are not related to the ring-down rate in the ring-down cavity and thus do not directly affect the CRDS measurement.
In conventional absorption measurements, when light passes through a sample of length l, the ratio of the transmitted and incident intensities, I.sub.t and I.sub.o, satisfies Beer's law: EQU .DELTA.I/I.sub.o =(I.sub.o -I.sub.t)/I.sub.o =1-e.sup.-.alpha.1,
where .alpha. is the absorption coefficient of the sample. Any intensity fluctuations will clearly result in uncertainties in the absorption measured. It is possible to define a minimum detectable absorption (MDAL) based on the intensity noise of the system as follows: EQU MDAL =.sigma..sub.l /l.sub.eff,
where .sigma..sub.I is the root-mean-square (RMS) intensity noise and l.sub.eff is the effective sample path length (e.g., in a multi-pass absorption measurement cell, the effective sample length can be many times the physical sample path length, since the light beam circulates inside the cell, passing through the sample many times, e.g., up to 500 times or more). Of course, more than one absorption measurement can be taken and the results averaged to reduce the measurement error, however, the fundamental limitation of the system being subject to intensity noise can not be overcome.
In CRDS the measured variable is the decay constant, .tau., or the ring-down rate 1/.tau., and thus the sensitivity is expressed as: EQU S.sub..tau. =.sigma..sub..tau. /(l.sub.eff F),
where F is the number of measurements taken per unit time and the units are expressed in cm.sup.-1 Hz.sup.-1/2. Clearly, intensity noise does not figure in this equation. In fact, the ultimate limit of CRDS is the fundamental barrier due to shot-noise inherent in the light beam. Shot-noise results from the discrete nature of photons making up the light beam. The photocurrent produced by a laser beam having power P is i=RP where R is the responsivity of the photodetector. For ideal detection, the photocurrent noise will directly reflect the shot noise of the light. The temporal distribution of shot-noise obeys Poisson statistics and can be expressed as: EQU .sigma..sub.I,shot-noise =(2el),
where e is the electronic charge (1.602.times.10.sup.-19 C).
Theoretically, if CRDS were only limited by shot-noise, the achievable sensitivity would be in the range of 10.sup.-14 cm.sup.-1 Hz .sup.-1/2 for a CRDS system having a 50 cm long cavity, a 10 mW continuous-wave (CW) laser with a 10 kHz linewidth and mirrors having losses of 50 ppm.
The actual performance of state-of-the-art CRDS in comparison to other conventional methods is illustrated in Table 1.
TABLE 1 Typical Spectroscopic Scheme MDAL (cm.sup.-1) Cost Complexity Single-pass absorption 10.sup.-6 low simple Multi-pass absorption 10.sup.-8 moderate simple ICLAS 10.sup.-6 -10.sup.-11 high difficult FM 10.sup.-6 -10.sup.-8 moderate moderate to difficult P CRDS 10.sup.-6 -10.sup.-10 moderate simple CW CRDS 10.sup.-8 -10.sup.-12 low to simple to moderate moderate ICLAS = intracavity absorption spectroscopy; FM = frequency modulation; P CRDS = pulsed CRDS; CW CRDS = continuous-wave CRDS
Most experimental CRDS setups have used pulsed laser sources (P CRDS). However, P CRDS has several practical disadvantages, which preclude shot-noise-limited detection, unless significant effort is made to eliminate them. First, most P CRDS arrangements are limited by the detector noise on the signal, unless special photodetectors such as photomultiplier tubes are used. Unfortunately, photomultiplier tubes can operate only in the ultra-violet to near-infrared wavelength ranges, so that P CRDS in the mid-infrared can be extremely limited. This detection noise is a direct consequence of the limited optical throughput of the high-finesse ring-down cavity. The optical throughput is a function of the ratio of the laser and cavity linewidths. Typical throughputs for pulsed lasers do not exceed 0.01%. In other words, this problem relates to the excess noise present on the ring-down signals, which makes the signal much more difficult to fit accurately. The greater this excess detector noise, the larger the error in the decay rate fit, and hence the greater the error in the absorption loss measurement.
Second, P CRDS is limited by the quality of the mode-matching between the laser beam transverse profile and the ring-down cavity modes. Ideally, only a single transverse and longitudinal cavity mode--the fundamental TEM.sub.00 mode--is excited in the ring-down cavity. However, because most pulsed laser linewidths tend to be large, multiple longitudinal modes can be excited if the ring-down cavity length is sufficiently large. Moreover, because it is difficult to accurately match the transverse profile of pulsed laser beams to the ring-down cavity mode geometry, multiple transverse modes become excited. Excitation of higher order modes, each having a distinct resonance frequency, can impose a sinusoidal beating which is superposed on the ring-down signal intensity exiting the ring-down cavity, unless all modes are perfectly collected onto a perfectly uniform detector. Physically, such detection is very difficult to implement. In addition, because each cavity transverse mode samples a different portion of the mirrors forming the cavity, each of the modes will experience slightly different reflection and diffraction losses in the cavity. Thus, multiple-mode excitation will also produce a superposition of exponentially decaying signals, each having a slightly different decay constant .tau.. Hence, trying to determine the decay constant .tau. for one particular mode, i.e., the fundamental mode, becomes difficult.
Third, the repetition rate of most pulsed laser systems is limited to 100 Hz, so that extensive averaging to improve sensitivity cannot be performed. Moreover, pulsed lasers tend to be bulky and expensive, and therefore impractical for commercial versions of P CRDS.
In addressing the first problem of P CRDS, CW CRDS uses a narrow line-width CW laser with external modulation to limit the optical noise by achieving high overlap between the laser linewidth and the ring-down cavity linewidth. The second problem of mode beating is limited by optically filtering the Cw laser beam profile to almost pure TEM.sub.00. The third problem is addressed by using repetition rates in excess of 1 kHz and up to 10 kHz thus permitting averaging operations. More information about these solutions can be found in D. Romanini et al. "CW Cavity Ring-down Spectroscopy", Chem. Phys. Lett., 264, p. 31 (1997); D. Romanini et al. "Cavity Ring-down Spectroscopy with an External Cavity Diode Laser", Chem. Phys. Lett., 270, p. 538 (1997); B. A. Paldus et al. "Laser Diode Cavity Ring-down Spectroscopy Using an Acousto-optic Modulator", J. Appl. Phys., 82, p. 3199, (1997); and U.S. Pat. No. 5,528,040 to K. K. Lehmann.
Unfortunately, the above improvements introduced in CW CRDS systems to overcome the problems associated with P CRDS have not resulted in significant improvements in the ability to perform spectral scans in real-time and, most importantly, have not managed to significantly improve the sensitivity of the CRDS technique. To date, the highest sensitivities obtained for P CRDS and CW CRDS do not approach the theoretical shot-noise limit. The best arrangements reported so far have sensitivities of about 8.times.10.sup.-10 cm.sup.-1 Hz.sup.-1/2 and 2.times.10.sup.-1 cm.sup.-1 Hz-1/2 respectively. These figures are still far short of the theoretical limits.
In terms of SNR, a ring-down decay signal is ultimately limited by the fluctuations in photon number that occur for a constant power level. For a power level of 1 mW, the shot-noise-limited SNR is 1.8.times.10.sup.6 :1, while for 1 .mu.W the SNR is 5.6.times.10.sup.4 :1. These figures are not achieved by state-of-the-art CRDS.
At this point, it should be noted that most CRDS arrangements, with the exception of a boxcar integrator arrangement (see D. Romanini et al., J. Chem. Phys., 102, p. 633 (1995)), as well as most other spectroscopy schemes utilize digital detection electronics. For example, U.S. Pat. No. 5,821,533 to Bingham et al. teaches immediate conversion of an exponentially decaying signal obtained in Ionizing Radiation Spectroscopy to a digital signal. In CRDS the exponentially decaying signal beam or ring-down beam from which the absorption data is derived is first sent to a photodetector which generates a corresponding current or voltage signal. The latter is digitized by a digitizer and passed on to digital processing electronics for determining the decay rate .tau. from which the absorption is determined. In this arrangement the technical noise of the photodetector and the detection electronics limit detection sensitivity. In fact, in this type of direct detection the ring-down signal decays into the noise of the detection electronics, which causes the electronic noise to become the limiting noise source.
In view of the above problems, it would be desirable to develop a CRDS scheme which permits one to approach the theoretical sensitivity limit of CRDS measurements. Specifically, it would be very desirable to provide a detection system for both P CRDS and CW CRDS whose primary limiting factor in determining the decay rate .tau. is the shot-noise present in the exponentially decaying ring-down beam.